According to the decimal bit value principle, the decimal part is written in the form without denominator, which is called
Do decimals. The point in the decimal is called the decimal point, which is the dividing line between the integer part and the decimal part of a decimal. The left part of the decimal point is an integer part and the right part of the decimal point is a decimal part. Decimals with zero integer parts are called pure decimals, and decimals with non-zero integer parts are called decimals. For example, 0.3 is a pure decimal and 3. 1 is a decimal.
Like integers, the counting units of decimals are arranged in a certain order, and their positions are called decimals.
Numbers. The numerical sequence is as follows:
There are two ways to read decimals: one is to read fractions, and the whole part with decimals is to read integers; small
The digital part is read by fractions. For example, 0.38 is pronounced as 38%, and 14.56 is pronounced as 14 and 56%. In another way, the integer part is still read as an integer, the decimal point is read as a "dot", and the decimal part reads the numbers on each digit in sequence. For example, 0.45 is read as 0.45; 56.032 is pronounced as 56.032.
The comparison method of decimal size is basically the same as that of integer, that is, the numbers on the same digit are compared in turn from the high position.
Therefore, to compare the sizes of two decimals, first look at their integer parts, and the larger the integer part, the larger the number; If the integer parts are the same, the one with the largest number in the tenth place is larger; If the deciles are the same, the percentile is larger;
Because decimals are decimal fractions, they have the following properties: ① Add or remove zero at the end of decimals, and the size of decimals.
No change. For example; 2.4 = 2.400, 0.060 = 0.06.② When the decimal point is shifted to the right by one, two and three places respectively, the decimal size will change, and the decimal value will be enlarged by 10 times, 1000 times and1000 times respectively. ...
Times; If the decimal point is shifted to the left by one place, two places and three places respectively, the decimal value will be reduced by 10 times, 100 times and 1000 times respectively. For example, expand 7.4 10 times to be 74, and expand 100 times to be 740. ..
Infinitely circulating decimals can only be expressed by fractions, such as 1/7, and all decimals can be expressed by fractions. Fractions are divided into finite decimals such as 1/5, infinite cyclic decimals such as 1/7, and infinite cyclic decimals such as 1/3.
Rational number: a number that can be accurately expressed as the ratio of two integers.
For example, 3, -98. 1 1, 5.72 ... and 7/22 are rational numbers.
Integers and fractions are rational numbers. Rational numbers can also be divided into positive rational numbers, 0 and negative rational numbers.
In the decimal representation system of numbers, rational numbers can be expressed as finite fractions or infinite cyclic fractions. This definition also applies to other decimals (such as binary). Encyclopedia of China (Mathematics)
Therefore, there is no contradiction.
Add "0" or remove "0" at the end of the decimal, and the size of the decimal remains the same. This is the so-called nature of the decimal.
Decimal times integer:
Convert decimal multiplication into integer multiplication calculation.
First, the decimal is expanded into an integer, and the product will be reduced by multiplying the expansion factor by the integer.
The decimal places of the product are related to the decimal places of the multiplicand. If the multiplicand has several decimal places, so does the product. Because to convert decimal multiplication into integer multiplication, the product will be amplified as many times as the multiplicand. So how many times must the product be reduced?
Calculate decimal multiplication with integers. First, calculate the product according to the calculation method of integer multiplication, and then see how many decimal places the multiplicand has. Count a few from the right of the product and point to the decimal point.
A decimal, starting from somewhere in the decimal part, and one or several numbers are repeated in turn. This decimal is called a cyclic decimal.
Circular part: the decimal part of a circular decimal, which is a number that appears repeatedly in turn.
It is called the cyclic part of this cyclic decimal. For example: 0.33 ... The loop part is "3"
2. 14242 ... The cyclic part is "42"
Pure cyclic decimal: the cyclic part starts from the first position of the decimal part.
Mixed cycle decimal: the cycle part does not start from the first position of the decimal part. (For example:
Blackboard book)
Simple notation: When writing cyclic decimals, for simplicity, only the cyclic part of decimals is written.
The first cycle part. If there is only one number in the loop, add a dot to this number; If there are multiple numbers in the loop part, please add a dot to the first and last numbers in this loop part.